1. You won't need to charge in store to check because...
2. ...yes the T610 battery has some charge in it
3. lithium polymer has a better life if is not totally drained so when it gets to 10% or so then stick it on charge.

The battery is partly charged but you shouldn't use the phone untill you charge it completely. The first time you charge, simply charge untill it stops charging. No point in having it in the charger longer then that since the charging circuits will be automatically cut off anyway.

As masseur said, the Li-Po batteries have no memory effect so there is no need to discharge the battery completely before you charge it again. However since the ammount of charges before the battery starts loosing performance is limited (500-1000 times), it might be a bad idea to stick it in the charger more then neccessary.

rhade: Yes, charge untill the battery indicator stops moving
Carlsb3rg: No negative effects, but you might want to minimize the number of charges to prolong battery life as much as possible. But it's really just a matter of convenience

I still use my original battery for my T68 purchased October 2001 and just leave it connected to the charger whenever i can... It has outlasted most people's batteries considering that they bought their units way later than mine.

Not quite wrath - the first time you charge the phone you should leave it on charge a couple of hours after the charge cycle appears to have been completed. The charging circuits aren't completely turned off at the 'end of charge' and the trickle charge is required to ensure that the whole cell is completely charged as the battery's circuitry won't be properly calibrated initially (and will indicate to the charger that charging is 'complete' before it actually is). The manual points out that you should leave the phone on charge for about 5 hours or so for the first charge IIRC. Charging after that should only take a couple of hours at most.